I think there's an error with the rotation matrix presented on page 33 of RVC 3rd edition 2023.
From my understanding, there's an error between the matrix form and the equation form of the rotation.
The equation reads:
xB=xA cos theta + yA sin theta
yB=-xA sin theta + yA cos theta
with the rotation matrix given as
Firstly, I'm not sure you can multiply a 2x1 matrix by a 2x2 matrix, but I'm happy to be corrected.
The top line of the matrix should be (cos theta sin theta) and the bottom should be (-sin theta cos theta) as we're rotating the reference frame clockwise.
What is listed in the book is the rotation of a vector within a reference frame.
I think there's an error with the rotation matrix presented on page 33 of RVC 3rd edition 2023.
From my understanding, there's an error between the matrix form and the equation form of the rotation.
The equation reads:
xB=xA cos theta + yA sin theta
yB=-xA sin theta + yA cos theta
with the rotation matrix given as
The top line of the matrix should be (cos theta sin theta) and the bottom should be (-sin theta cos theta) as we're rotating the reference frame clockwise.
What is listed in the book is the rotation of a vector within a reference frame.